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1 Research Division Federal Reserve Bank of St. Louis Working Paper Series The Great Housing Boom of China Kaiji Chen and Yi Wen Working Paper C August 2014 Revised August 2016 FEDERAL RESERVE BANK OF ST. LOUIS Research Division P.O. Box 442 St. Louis, MO The views expressed are those of the individual authors and do not necessarily reflect official positions of the Federal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors. Federal Reserve Bank of St. Louis Working Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to Federal Reserve Bank of St. Louis Working Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.

2 The Great Housing Boom of China By KAIJI CHEN AND YI WEN China s housing prices have been growing nearly twice as fast as national income over the past decade, despite a high vacancy rate and a high rate of return to capital. This paper interprets China s housing boom as a rational bubble emerging naturally from its economic transition. The bubble arises because high capital returns driven by resource reallocation are not sustainable in the long run. Rational expectations of a strong future demand for alternative stores of value can thus induce currently productive agents to speculate in the housing market. Our model can quantitatively account for China s paradoxical housing boom. Housing prices in China have experienced rapid and prolonged growth in the recent decade, rising nearly twice as fast as people s disposable income. Data for thirty-five major Chinese cities show that average real housing prices have grown at an annual rate of around 17 percent over the past decade, much higher than the average income growth rate of 11 percent across the thirty-five cities and the nation s 10 percent average gross domestic product (GDP) growth in the same period. Closely associated with the housing boom is the growing vacancy rate across Chinese cities, which reached a national average of 22.4 percent in Yet during the same period, China has also enjoyed a very high rate of return to capital. For example, between 1998 and 2012, China s real rate of return to capital (net of depreciation) was constantly around 20 percent or above. The combination of these features namely, (i) real housing prices outpacing income for a decade; (ii) a high vacancy rate, and (iii) a high rate of return to capital is puzzling. A standard neoclassical model, even with an inelastic housing supply, predicts that housing prices would grow at most as fast as aggregate income; thus this type of models can hardly explain China s fast housing price growth and its high national vacancy rate. Alternatively, although the classical Samuelson-Tirole bubble model may explain the high vacancy rate in China, it requires the critical assumption that the rate of return to capital be so low that holding an intrinsically valueless bubble asset would be rational. Chen: Economics Department, Emory University, 1602 Fishburne Drive, Atlanta, GA ( kaiji.chen@emory.edu), and the Research Department of the Federal Reserve Bank of Atlanta. Wen: Research Division, Federal Reserve Bank of St. Louis, P.O. Box 422, St. Louis, MO, ( yi.wen@stls.frb.org), and School of Economics and Management, Tsinghua University. We thank three anonymous referees for their very helpful comments and suggestions; Xiangyu Gong, Xin Wang, and Tong Xu for capable research assistance; Jing Wu for sharing data on China s housing prices; and Suqin Ge and Dennis Tao Yang for sharing data on China s real wage rate. We thank Toni Braun, Satyajit Chatterjee, YiLi Chien, Carlos Garriga, Lee Ohanian, B. Ravikumar, Manuel Santos, Zheng Song, Kjetil Storesletten, Gian Luca Violante, Yikai Wang, Tao Zha, and participants of the Brown Bag Seminar at the Federal Reserve Bank of St. Louis; 2013 Tsinghua Macro Workshop; 2013 Shanghai Macro Workshop; 2014 Spring Housing-Urban-Labor-Macro (HULM) conference; and 2014 Northwestern-SAIF Conference in Macroeconomic Policies and Business Cycles for helpful comments. The views expressed in this paper are those of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or the regional Reserve Banks. 1

3 2 AMERICAN ECONOMIC JOURNAL MONTH YEAR But such an assumption is at odds with the prolonged high rate of return to capital in China. In this paper, we propose a theory to explain the paradoxical housing boom in China. The key ingredient in our model is a transition stage featuring massive labor reallocation (after economic reform) from a conventional less productive sector to an emerging sector consisting of productive but financially constrained entrepreneurs. The rate of return to capital in the emerging sector remains persistently high during the transition stage because of the large pool of surplus labor gradually unleashed from the traditional sector. However, such high capital returns driven mainly by resource reallocation are clearly unsustainable in the long run. Thus, rational expectations of a significantly lower rate of return to capital in the remote future can induce current generations of entrepreneurs to seek alternative stores of value for their rapidly growing wealth. In a financially underdeveloped economy with a limited supply of financial assets, housing becomes a natural investment option for currently productive entrepreneurs they rationally anticipate a strong demand for such an asset by future generations. This sustains a self-fulfilling growing housing bubble, with growth rates significantly higher than the average disposable income during the transition despite very high returns to capital. We show that such a model, calibrated to match China s major macroeconomic features, such as GDP growth and labor market dynamics, can quantitatively replicate China s housing price dynamics over the past decade fairly well and still be consistent with many other salient features of the Chinese economy. Our theory also predicts that such a fast-growing housing bubble will lose steam as the economy approaches the Lewis turning point with exhausted surplus labor in the rural areas. This prediction is consistent with the recent labor market and housing market data from China. Our paper fits into the fast-growing literature on economic development and resource misallocation under financial frictions. 1 While the bulk of the literature emphasizes the effects of resource reallocation on improving allocative efficiency and the associated saving investment dynamics during the transition, we argue that such a transition may also be prone to asset bubbles, especially growing bubbles, even when the economy enjoys fast productivity growth and high returns to capital. This prediction is also supported by evidence from other emerging economies in Asia, such as Korea, Taiwan, and Vietnam, which experienced housing bubbles during their respective economic transition periods featuring labor reallocation from traditional less productive sectors to the emerging and more productive sectors. Our model is based on that of Song, Storesletten, and Zilibotti (2011, SSZ hereafter). The SSZ model is attractive for our purposes because it can endogenously generate and quantitatively account for some important features of China s economic transition, such as a persistently high rate of return to capital in the emerging sector, which we argue are key to understanding China s prolonged paradoxical housing boom. Our contribution and value added is to show that such a development path can sustain growing bubbles 1 See, for example, Jeong and Townsend (2007); Restuccia and Rogerson (2008); Guner, Ventura, and Xu (2008); Song, Storesletten, and Zilibotti (2011); Buera, Kaboski, and Shin (2011); Buera and Shin (2013); Moll (2014); and Midrigan and Xu (2014).

4 VOL. VOL NO. ISSUE THE GREAT HOUSING BOOM OF CHINA 3 bubbles that grow much faster than aggregate income for a long period despite a persistently high rate of return to capital. Our paper is one of the first to study growing bubbles, as opposed to static bubbles or bubbles that grow at or below the growth rate of the economy. 2 In addition, our model sheds light on the economic and welfare implications of China s housing bubble: It can significantly prolong China s economic transition and reduce social welfare. Unlike many traditional bubble models where bubbles are welfare improving because of dynamic inefficiency, bubbles in our model can exist even when the economy is dynamically efficient, thanks to a disparity between social and private rates of return to capital. 3 Hence, by crowding out private capital formation and other productive activities, the growing bubble in our model crowds out productive investment, prolongs economic transition, and reduces average welfare. Our paper also contributes to the emerging literature on China s high housing price puzzle. Most theoretical works in this area focus on why the housing price level is so high in China. 4 In sharp contrast, our paper focuses on why housing prices in China have been able to grow much faster than the average disposable income over a prolonged period. 5 By shifting the analysis from the level of housing prices to the growth rate of housing prices, our paper sheds light on China s housing price dynamics, as well as why such a growing housing bubble may create resource misallocation and prolong China s economic transition, which is an issue unaddressed in the literature. The remainder of the paper is organized as follows: Section I presents some institutional background and stylized facts about China s housing market to frame the questions we raise and support the key assumptions in our theoretical model. Section II describes a simple two-period benchmark model to illustrate our essential explanations of the housing boom, as well as the model s qualitative implications. Section III extends the analysis to a multi-period model for calibration and quantitative analysis. Section IV concludes with remarks for further research. The online Appendix contains proof of all Propositions and Lemmas. 2 For the rapidly developing literature on housing bubble, see Caballero and Krishnamurthy (2006); Kocherlakota (2009); Farhi and Tirole (2012); Giglio and Severo (2012); Martin and Ventura (2012); Ventura (2012); Burnside, Eichenbaum, and Rebelo (2013); Miao and Wang (2013); and Galí (2014) among many others. 3 See also Farhi and Tirole (2012) for a similar result. In both that paper and ours, agency frictions drive a wedge between the social rate of returns to capital and the equilibrium rate of return. Accordingly, bubbles exist even in an environment with dynamic efficiency. However, the reason that bubbles may reduce welfare differs between our paper and theirs. In their paper, the presence of bubbles raises the equilibrium interest rate, which reduces the price of other external liquid assets. 4 See, for example, Wei, Zhang, and Liu (2012). 5 Using income growth as a benchmark for housing price growth implies that (i) disposable income serves as a demand-side factor on housing prices and (ii) housing supply is relatively inelastic with respect to housing prices. See Hurst (2015) for such a model. The relatively inelastic housing supply is consistent with the institutional features in China. Specifically, the supply of constructible land in China is monopolized by the local government, which is subject to land quotas to urbanize rural land. Moreover, housing units at different locations and even different floor levels are essentially heterogeneous goods. Such a feature limits the substitutability of housing across Chinese cities or even across different districts within a city. As a result, housing markets in China are highly localized, which further reduces the price elasticity of the housing supply. In fact, the housing price index we examine in this paper is constructed using the hedonic method, which has been controlled for changes in complex-level attributes over time, including distance to a city center, the floor area ratio, etc. Accordingly, changes in such housing prices are reasonably isolated from pure changes in the housing/land supply caused by suburbanization or higher floor-area ratios, as recently observed in China.

5 4 AMERICAN ECONOMIC JOURNAL MONTH YEAR I. Stylized Facts A. Housing Price Growth and the Vacancy Rate It is well-known that the official housing price indices published by the Chinese government suffer from many measurement problems and do not control for housing quality. Hence, they tend to underestimate the growing trend of China s housing prices. 6 To correct such problems, Wu, Deng, and Liu (2014) use independently constructed housing price indices based on sales of newly built housing units in thirty-five major Chinese cities. These city-level series are then aggregated into a national indicator using a weighted-average formula, with the total transaction volume during in each city as the weight. The resulting national housing price index shows a much faster growth rate than the official housing price index. For example, the national real housing price index increased 17 percent per year between 2006:Q1 and 2010:Q4. If we ignore the negative impact of the 2008 financial crisis, the average growth rate of housing prices was about 20 percent per year during this period (see Figure 1, solid line with circles). [Insert Figure 1 here] The increase in housing prices in China is also accompanied by rapidly rising land prices. Figure 1 (dashed line with stars) shows that nationwide real constant-quality land values have grown at an average rate of more than 16 percent per year between 2004:Q1 and 2013:Q2. In particular, between 2006:Q1 and 2010:Q4, a period for which housing price data is available, land prices grew at an average rate of 26 percent, much faster than the housing price growth during the same period. Accordingly, rising land values have constituted an important and increasing share in housing prices. For example, according to Wu, Gyourko, and Deng (2012), in the city of Beijing, land values averaged 37 percent of housing prices before 2008 and rose above 60 percent after Such a growth pattern of housing prices is prevalent across almost all major cities in China. Figure 2 shows that most of the thirty-five major cities in China have experienced a significantly faster growth rate in housing prices than city-level aggregate disposable income, which takes into account population growth due to migration. For example, in large cities such as Shanghai and Beijing, the average real growth rate of housing prices during the same period is two to three times larger than the respective real growth rate of disposable income. The fact that house prices grew persistently faster than aggregate disposable income at both the national and city levels casts doubt on the conventional wisdom that China s housing price growth is driven mainly by the increased utilitarian demand for housing due to rural-to-urban migration or solely by the rapidly increasing purchasing power of Chinese citizens. 7 6 For example, the National Bureau of Statistics of China (NBSC) provides two major housing price indices. Based on these housing price indices, the average growth rate of housing prices in China is below the average growth rate of the economy. However, Wu, Deng, and Liu (2014) argue that these measures are severely biased downward because they fail to control both the complex-level quality changes (e.g., housing suburbanization) and unit-level quality changes (e.g., developer pricing strategies). 7 See Garriga, Tang, and Wang (2014) for the migration view of China s housing price boom.

6 VOL. VOL NO. ISSUE THE GREAT HOUSING BOOM OF CHINA 5 [Insert Figure 2 here] In a more recent empirical study, Fang et al. (2015) use an independent data source for 120 Chinese cities to document the patterns of housing price growth and local per capita aggregate income growth in the sample period Among other things, they found that housing prices grew persistently faster than per capita disposable income or gross regional product in the first- and second-tier cities in China. 8 Such evidence is consistent with that presented by Wu, Deng, and Liu (2014). Along with the housing boom is the continuously rising and high housing vacancy rate. According to the China Household Finance Survey (2014, CHFS hereafter), in 2013 the average vacancy rates in the first-, second-, and third-tier cities in China were 21.2 percent, 21.8 percent, and 23.2 percent, respectively. 9 Among different groups of households, 35.1 percent of entrepreneurial households own vacant houses. Furthermore, the proportion of households with vacant houses increases with household income. In the top decile income group, for example, 39.7 percent of households have vacant houses, which is about 22 percentage points higher than households in the lowest income quartile. Housing prices growing faster than income implies a rapidly rising price-to-income ratio for average wage earners. Ge and Yang (2014) use data from the China Household Income Survey (2014) and find that the growth rate of real wages has been increasing since the economic reform in Between 1998 and 2007, average real wage growth reached 9.0 percent per year, almost as fast as real per capita GDP growth. However, housing prices have been growing much faster (nearly twice as fast the gap between real housing price growth and real wage growth is more than 8 percentage points). 10 B. Returns to Capital and Resource Reallocation It is well documented that the average real rate of return to capital in China has remained around 20 percent over the past decade (see, for example, Bai, Hsieh, and Qian, 2006). We reconfirm this finding here by constructing the real rate of return to capital following the approach of Bai, Hsieh, and Qian (2006). 11 Panel A of Figure 3 shows that the real rate of return to capital was on average 20 percent between 1998 and In particular, it increased steadily from 18 percent in 2001 to 26 percent before the start of financial crisis in Similarly, the measured after-tax real rate of return to capital (excluding urban housing) averaged about 18.2 percent between 1998 and 2012, approx- 8 China s first-tier cities usually refer to Beijing, Shanghai, Guangzhou, and Shenzhen, which constitute The Big 4. Second-tier cities include the provincial capital cities and other municipalities directly under the central government. Third-tier cities include all other cities. 9 The definition of vacancy rate in CHFS is the same as the homeowner vacancy rate defined in the U.S. Census Bureau s Housing Vacancies and Homeownership Survey (see CHFS, 2014). Specifically, it is calculated as the proportion of the homeowner inventory that is vacant and for sale. Hence, the definition of vacant housing units does not include housing units that are newly built but not yet sold, or empty housing for parents and children, or for leisure. 10 According to the data from the NBSC, the national average growth rate of real per capita disposable income between 1998 and 2012 was 9.3 percent per year. 11 Specifically, we measure the capital-to-output ratio at market prices and include any expected change in the price of capital as part of its returns. Our computed series of the real rates of returns to capital between 1998 and 2005 are essentially the same as those of Bai, Hsieh, and Qian. (2006).

7 6 AMERICAN ECONOMIC JOURNAL MONTH YEAR imately the same as the estimated growth rate of the aggregate housing prices in real terms. 12 Underlying the enduring high rate of return to capital is the massive labor reallocation in China. Panel B of Figure 3 plots the evolution of the share of private employment in total employment. Following SSZ, we adopt two measures of the private employment share: (i) the share of domestic private enterprises (DPE) in total employment (which equals employment in DPE plus state-owned enterprises); and (ii) (DPE+FE)/(DPE+FE+SOE+COE), where FE is employment of foreign enterprises, COE is that of collectively-owned enterprises, and SOE is that of state-owned enterprises. For both measures, the private employment share increased steadily for most years during the period and surpassed 60 percent in [Insert Figure 3 here] C. Empirical Evidence Consistent with the Marginal Investor Hypothesis A crucial premise in our theoretical bubble model that explains the three stylized facts of China s housing boom is the marginal investor hypothesis the fast growth rate of housing prices (despite high returns to capital and a high vacancy rate) is mainly driven by the speculative housing demand from agents (entrepreneurs) in the productive sector of the economy, who have access to high returns to capital. Hence, the higher the private rate of return to capital, the faster housing price growth outpaces aggregate income growth. A stylized fact of China s housing boom is that owners or investors holding vacant housing units consist not only of middle-income and high-income households, but also entrepreneurs and firms, including the most productive and profitable firms. Standard economic theories would find this phenomenon puzzling it is paradoxical that well-todo entrepreneurs and productive firms with high capital returns would engage in speculative housing (or real estate) investment. Furthermore, such theories would find it even more puzzling that private firm returns to capital across different cities are positively correlated with or predictive of these cities housing price growth outpacing local aggregate income growth. In what follows, we document precisely these stylized facts from three different perspectives. First, we use household-level evidence to show the predictive power of entrepreneurial status in the vacancy rate of a city s housing market. Second, we conduct cross-city panel regression analysis to show a strong empirical linkage between excess housing price growth defined as the growth rate of housing prices minus the growth rate of aggregate disposable income and the rate of return to capital facing private firms across different regions. Finally, we use firm-level data to reveal the extent of firm involvement in real estate investment and the linkage between their returns to capital and ownership structure. 12 The measured after-tax returns to capital excluding urban housing are computed by excluding the urban residential capital stock from the measured capital stock and by excluding imputed rent (assumed by the NBSC to be 3 percent of the original value of the residential capital stock) and tax on output and enterprise income from the capital income.

8 VOL. VOL NO. ISSUE THE GREAT HOUSING BOOM OF CHINA 7 HOUSEHOLD EVIDENCE. As noted, China s average vacancy rate was at least as high as 22.4 percent across cities in 2011, implying that nearly a quarter of privately-owned housing units in China are unoccupied (by owners or renters). What explains such a high homeowner vacancy rate? The CHFS, which conducts a regression of housing vacancy status against an exhaustive list of both household-level and macro-level variables, shows that a homeowner s entrepreneurial status (i.e., whether the homeowner owns a private business) has strong predictive power on the vacancy status of housing units in all Chinese cities. In other words, entrepreneurs with access to alternative assets (capital) are more likely to own vacant housing units than other types of homeowners. This fact holds true even if the regressions control for household income, the education level of the household head, the household s attitude about risky investments, the housing price-torent ratio, the urbanization rate, and whether the household has unmarried male members (see Table 1 of CHFS, 2014). Note that entrepreneurs account for 17 percent of China s urban population and that, conditional on holding vacant housing units, 25 percent of homeowners are entrepreneurs. CROSS-CITY EVIDENCE. In our model, the marginal investors in the housing market are the entrepreneurs who have access to high returns to capital and yet decide to also participate in the housing market. This implies that the rate of returns to capital facing the marginal investor will dictate the rate of return to housing investment in a self-fulfilling housing bubble equilibrium by the no-arbitrage condition. The concept of the marginal investor in our model is borrowed from the asset pricing literature, where the rate of return to risky assets is determined by a marginal investor able to participate in such an asset market with no borrowing constrained. As far as we know, the best empirical approach to support the marginal investor theory in the asset pricing literature is to assess the predictive power of the investor s marginal value of wealth (proxied by their leverage position) on excess asset returns (see, for example, Adrian, Etula, and Muir, 2014). Here we follow a similar strategy by investigating the predictive power of private capital returns in different cities on excess housing price growth. Our empirical findings suggest that: (i) across major Chinese cities, the private rate of return to capital is a strong predictor of the city s excess housing price growth; and (ii) capital returns of private firms have larger and more significant predictive power on excess housing returns than do capital returns of SOEs. Specifically, we measure returns to capital in a region as the ratio of total profit to the net value of fixed assets. We run a panel fixed-effect regression of excess housing price growth against returns to capital of different types of firms in thirty-five major cities in China between 2006 and Columns (1) and (2) of Table 1 suggest that returns to capital are highly significant predictors of excess housing returns regardless of firm type (ownership). Column (3) shows that when both SOE and privately-owned firms are included as independent variables, the returns to capital of private enterprises are more significant and stronger predictors of excess housing price growth than SOE. This evidence suggests that private enterprises are more likely than SOE to be marginal investors in the housing market.

9 8 AMERICAN ECONOMIC JOURNAL MONTH YEAR [Insert Table 1 here] FIRM EVIDENCE. Firm-level data show that a substantial fraction of non-real estate firms (including very productive ones) in China engage in real estate investment unrelated to their original business. This stylized fact indicates not only a close link between returns to capital and housing returns, but also a possible source of the crowding-out effect the housing bubble has on capital investment (as we show in the next section). Here we use data on publicly listed firms, from the China Stock Market and Accounting Research (CSMAR) database, to check the extent non-real estate firms are involved in real estate investment and issues related to our marginal investor hypothesis. We restrict our sample to firms that have been traded for at least two years on the China A-share stock market over the period We exclude firms in the real estate and construction sectors. As shown in Table 2, about 45 percent of firms have such investment properties (purchased for rent and capital gain, instead of as a necessary input or production factor in their own business). 14 The share averages about 15 percent of these firms total physical assets and is stable over time. [Insert Table 2 here] We now examine the difference in returns to capital across firm ownership types for all firms investing in the housing market. Our empirical evidence shows that SOE on average have lower capital returns than private firms, whih is consistent with our model. Specifically, we regress capital returns against the degree of state ownership. We construct capital returns at the firm level using the ratio of operating profit to the one-period lag of property, plants, and equipment (PPE), which have been excluded from the value of investment property since We adopt three different measures to gauge the degree of state ownership. The first is a direct measure of the state-owned stock share and the second and third measures pertain simply to state-ownership dummies. For the second measure, the state-ownership dummy takes a value of 1 if its state-owned stock share exceeds 50 percent. For the third, the dummy takes a value of 1 if the state-owned stock share exceeds 25 percent. To be consistent with our model s assumption, we also add a one-digit industry dummy. 15 As Table 3 shows, for all three measures, the rate of return 13 Since January 1, 2007, all listed firms in China have been required to disclose their real estate holdings for investment purposes, which includes any land and buildings held for rental income and/or for capital appreciation. 14 As mentioned by Li, Shao, and Tao (2015), prominent examples of non-real estate firms diversifying into real estate include Youngor (a leading garment company), Kweichow Moutai (a leading liquor company), and Suning (a leading electronics retailer). 15 The empirical model is K P it = cons + β S it + γ j I nd_dum j i + ε it, j J where K P denotes the capital returns, S it is the measure of the degree of a firm s state ownership, and I nd_dum is the industry dummy.

10 VOL. VOL NO. ISSUE THE GREAT HOUSING BOOM OF CHINA 9 to capital is indeed negatively correlated with the degree of state ownership among the firms investing in real estate. 16 [Insert Table 3 here] To sum up, the empirical evidence presented in this section supports our marginal investor hypothesis: (i) entrepreneurs or productive firms are extensively involved in the housing market and are an important determinant of China s high vacancy rate; (ii) private capital returns are highly predictive of the excess housing price growth across major cities in China; and (iii) on average, the returns to capital of SOE (that invest in the housing market) are lower than those of private firms and less predictive of excess housing price growth across major cities, suggesting that private firms tend to be the marginal investors. D. Crowding-out Effects on Capital Investment Data from the China Statistical Yearbook (2012, CSY hereafter) show that total real estate investment as a share of GDP increased by more than threefold, from 4.2 percent in 1999 to 13.2 percent in 2011, with residential investment accounting for about 70 percent of the boom. The average nominal growth rate of residential investment was 25.5 percent per year, compared with 13.9 percent for nominal GDP. Accordingly, the share of residential investment in GDP rose fourfold from 2.4 percent in 1999 to 9.5 percent in On the other hand, the rapidly growing housing bubble has shown a strong crowdingout effect on China s capital formation for both SOE and private firms. We measure this effect by estimating the correlation coefficients between real housing price growth (deflated by the consumer price index) and non-real estate investment growth (deflated by the producer price index). 17 To remove seasonal effects, we use year-over-year growth rates at monthly frequency. Table 4 shows that the growth of real estate investment is significantly and positively correlated with housing price growth, while non-real estate investment is significantly negatively correlated with housing price growth. More importantly, the results show that the current growth in housing prices is a strong predictor of a future decrease in nonreal estate investment growth, with the peak correlation between housing price growth and investment growth reached at a five-month lead. This crowding-out effect of housing price growth on non-housing investment is consistent with our model s predictions, 18 and also supported by independent empirical studies. For example, Li, Shao, and Tao (2015) find that firms with real-estate investment property tend to under-invest by 10 percent in fixed capital formation compared with their industry benchmark. Wu, Gyourko, and 16 This does not rule out the possibility that in some industries monopolized by SOE (e.g., petroleum), SOE investing in the property market can also enjoy very high revenue-based productivity. 17 Due to data availability constraints, we are only able to decompose aggregate investment into real estate investment and the rest. 18 A wide class of models (e.g., Kocherlakota, 2009, and Martin and Ventura, 2012) predicts that housing bubbles, by serving as collateral, crowd in (instead of crowding out) capital investment.

11 10 AMERICAN ECONOMIC JOURNAL MONTH YEAR Deng (2015) find that, for publicly-listed firms, real estate value has no impact on fixed capital investment via the collateral channel. Similarly, Chen, Liu, and Zhou (2013) provide empirical evidences that increases in real estate prices tend to crowd out firms fixed capital formation in China. [Insert Table 4 here] E. Other Facts Concerning the Model Assumptions Our model makes the following simplifying assumptions: both the land supply and the interest rate are fixed. In addition, our model focuses on housing price dynamics over the past decade, which correspond to a period of massive SOE privatization in China. Land Supply. Land available for home construction in China is strictly controlled by the government. During , land available for new construction was limited to 20.4 million acres; during , it was limited to no more than million acres. These restrictions on the size and new release of construction land were further strengthened by the National Land Use Plan , passed by the State Council of China in August According to this regulation, the total land available for construction in urban and rural areas is limited to million acres by 2010 and million acres by The same plan requests that the amount of cultivated land in 2010 and 2020 be maintained at billion acres and billion acres, respectively, the so-called redline lower limit for the total amount of arable land. As shown in Figure 4, since 2003, the amount of arable land has more or less stabilized, implying a de facto fixed supply of land for home and real estate construction. [Insert Figure 4 here] Financial Underdevelopment. In our model, access to cheap credit allows SOE to survive despite much lower productivity than private firms. In China, the interest rate is controlled by the central bank to facilitate cheap credit to SOE. As shown in Figure 5, China s interest rates are essentially flat with the deposit rate substantially below the lending rate. [Insert Figure 5 here] In addition, the availability of financial assets as vehicles of household savings is quite limited in China: Stock markets are poorly regulated and dominated by SOE, the national capital account is closed, and the exchange rate is fixed or tightly managed. Accordingly, household savings consist mainly of bank deposits, which are channeled through stateowned banks to the conventional sector occupied mainly by SOE. 19 Through a system of strict capital controls, where the state directly manages the banking sector and financial 19 The household savings rates in China averaged 25 percent between 1998 and 2009 (Curtis, Lugauer and Mark, 2015) and bank deposits were the major share of household financial assets (e.g., 75 percent in according to Yi and Song, 2008).

12 VOL. VOL NO. ISSUE THE GREAT HOUSING BOOM OF CHINA 11 intermediation, the government has been able to maintain or suppress interest rates at below market-clearing levels. SOE Reform. SOE reform starting in 1997 helped to release cheap labor from the state sector to the private sector, which has sustained the high private returns to capital during China s economic transition. Under China s planned economy, SOE were the major employers in cities and played the pivotal role of maintaining low unemployment and ensuring social stability. As a result, even unprofitable SOE could survive. By the mid-1990s, the Chinese government realized that its gradualist reform policy could no longer manage the mounting losses of SOE. Beginning in 1997, China moved forward with more aggressive restructuring of large SOE, accomplished through large-scale privatization. The reallocation of labor and capital from SOE to private firms has been a key source of productivity growth in the past decade. II. The Benchmark Model In this section, we develop a theory of China s housing boom consistent with the institutional background and stylized empirical facts about China and its housing market behavior. In particular, we extend the SSZ model to a setting with an intrinsically valueless asset housing and prove that a housing price bubble that grows faster than GDP exists even if housing provides no rents or utilities to investors. For simplicity, we exclude low-income households (workers) from the housing market because their participation has only a level effect but no growth effects on the housing prices. We emphasize a growing bubble because the traditional bubble literature often focuses exclusively on static bubbles or bubbles that grow at most at the same rate as the economy, which is contradicted by the Chinese data. In this section, we illustrate our main story in a twoperiod overlapping-generations (OLG) model. We extend the model to a more realistic setting with multi-period OLG for the quantitative analysis in Section 4. A. The Environment The economy is populated by two-period lived agents with overlapping generations. Agents work when young and consume their savings when old. Agents have heterogeneous skills. In each cohort, half of the population are workers without entrepreneurial skills and the other half are entrepreneurs. Entrepreneurial skills are inherited from parents; we do not allow transition between social classes (for simplification without loss of generality). The total population, N t, grows at an exogenous rate ν. Before the economy starts, the government owns a fixed H unit of housing (land). At the beginning of the first period, the government sells the housing stock to the market (if there is demand) and consumes the proceeds. We assume that foreign capital cannot flow freely into China under capital controls, which rules out foreigners speculating in China s housing market. TECHNOLOGY. There are two production sectors and thus two types of firms. Labor is perfectly mobile across the two sectors but capital is not. The first sector is composed

13 12 AMERICAN ECONOMIC JOURNAL MONTH YEAR of conventional firms F-firms, which, for simplicity, are owned by a representative financial intermediary (e.g., a state-owned bank) and operated as standard neoclassical firms. 20 The second sector is a newly emerging private sector composed of unconventional firms E-firms, operated by entrepreneurs. More specifically, E-firms are owned by old (parent) entrepreneurs, who are residual claimants on profits, and they hire their own children as managers. Workers can choose to work for either type of firm. E-firms are more productive than F-firms but are borrowing constrained they cannot borrow from each other or from any other sources. As a result, E-firms must self-finance capital investment through their own savings. In contrast, F-firms can rent capital from their representative financial intermediary at a fixed interest rate, R. Accordingly, F- firms can survive in the short run despite inferior technology. Over time, however, labor will gradually reallocate from F-firms to E-firms as the capital stock of E-firms expands. Thus, the economy features a transition stage during which F-firms and E-firms coexist, but the F-sector is shrinking and the E-sector is expanding. When the transition ends, only E-firms exist and the economy becomes a representative-agent growth model with neoclassical features. Our focus in this paper is the transition stage. 21 The technologies of the two types of firms follow constant returns to scale, (1) y F t = ( k F t ) α ( At n F t ) 1 α, y E t = ( k E t ) α ( At χn E t ) 1 α, where y j, k j, and n j denote per capita output, capital stock, and labor, respectively, for a type- j firm, j {E, F}. The parameter χ > 1 captures the assumption that E-firms are more productive than F-firms. Technological growth in both sectors is constant and exogenous and given by A t+1 = A t (1 + z). However, during the economic transition, resource reallocation can generate endogenous growth faster than growth in A t. WORKER S PROBLEM. Workers can deposit their savings into the representative bank and earn a fixed interest rate, R. However, workers cannot borrow from banks. Without loss of generality, we also assume that workers do not speculate in the housing market. Allowing workers to invest in housing does not change our main results although the housing price level would be much larger, the growth rate of housing prices would be unaffected. 22 This result stays the same because the equilibrium growth rate of housing prices in our model is determined by the rate of return to capital of the entrepreneurs, who are the marginal investors in the bubbly equilibrium. 20 We can assume that F-firms have market power and our main results do not change qualitatively. 21 Note that the concept of transition in this paper is different from the convention in the neoclassical growth model, where transition means the dynamic path from an initial point toward the steady state. This conventional transition phase shows up in our model after the F-sector disappears. To avoid confusion, we call this neoclassical transition period post-transition. 22 The proof is available upon request.

14 VOL. VOL NO. ISSUE THE GREAT HOUSING BOOM OF CHINA 13 The worker s consumption-saving problem is (2) max log c c1t w 1t w + β log cw 2t+1,cw 2t+1 subject to c1t w + sw t = w t and c2t+1 w = sw t R, where w t is the market wage rate; c1t w, cw 2t+1, and st w denote, respectively, consumption when young, consumption when old, and the worker s savings. THE F-FIRM S PROBLEM. In each period, an F-firm maximizes profits by solving the following problem: (3) max k F t,n F t ( k F t ) α ( At n F t ) 1 α wt n F t Rk F t, where R represents either the rental rate for capital or the deposit rate that is, the two rates are the same. The first-order conditions imply (4) w t = (1 α) A t ( α R ) α 1 α. Note that during the transition, the wage rate, scaled by the level of technology, w t /A t, is constant due to a constant rental rate for capital and, accordingly, a constant capitalto-labor ratio, kt F / ( ) A t nt F 1 = (α/r) 1 α. When the transition is completed, all F-firms disappear, so equation (4) no longer holds. THE E-FIRM S PROBLEM. Following SSZ (2011), we assume that young entrepreneurs receive a management fee, m t, from their parents, which is a fixed ψ < 1 fraction of the output produced, m t = ψ ( ) kt E α ( ) 1 α. At χnt E 23 Therefore, the old entrepreneur s problem can be written as (5) max (1 ψ) ( k E nt E t ) α ( At χn E t ) 1 α wt n E t. 23 SSZ also provide a micro-foundation for a young entrepreneur s management fee as a fixed fraction of output: there exists an agency problem between the manager and owner of the business. The manager can divert a positive share of the firm s output for her own use. Such opportunistic behavior can be deterred only by paying managers a compensation that is at least as large as the funds they could steal, which is a share ψ of output. An alternative interpretation of ψ is that it reflects the government policy that transfers resources from the capital owners (the old entrepreneurs) to the managers (the young entrepreneurs). See Miao, Wang, and Zhou (2016), who study housing bubbles based on firm-level policy distortions.

15 14 AMERICAN ECONOMIC JOURNAL MONTH YEAR The first-order conditions imply a linear relationship between n E t and k E t : (6) n E t = [(1 ψ) χ] 1 α ( ) 1 R 1 α α k E t χ A t. Such a linear relationship is obtained because of a constant wage rate, which results from the constant interest rate, R. Accordingly, labor is reallocated to E-firms at a speed equal to the growth of E-firm capital stock. Substituting (6) into (5) gives E-firm profit: π ( ) kt E 1 1 α = (1 ψ) α χ α Rkt E ρ E kt E, where the first equality is based on equation (6). Whenever F-firms exist, the return to capital for E-firms, ρ E (1 ψ) α 1 1 α χ α R, is a constant because nt E increases linearly in kt E. Similar to SSZ, we impose the following assumption about E-firm relative productivity, such that an entrepreneur s return to capital is higher than the deposit rate, R, during the transition: χ > χ (1 ψ) 1 α 1. THE YOUNG ENTREPRENEUR S PROBLEM. The young entrepreneur decides consumption and portfolio allocations in housing investment, bank deposits, or physical capital investment. The rate of return to capital investment is simply ρ E. We assume that the balanced growth rate, which equals the rate of return to housing investment at a steady state, is greater than the bank deposit rate that is, (1 + z) (1 + ν) > R. As a result, the entrepreneur will always prefer investing in housing to depositing funds in the bank. Given housing prices, Pt H, the young entrepreneur faces a two-stage problem. In the first stage, a young entrepreneur s consumption-saving problem is: (7) max s E t log ( ) m t st E + β log R E t+1 st E, where Rt+1 E max { ρ E, Pt+1 H /P } t H is the rate of return for entrepreneur s savings and depends on the entrepreneur s portfolio choices. First-order conditions give the optimal savings of the young entrepreneur, st E = m t / ( 1 + β 1). In the second stage, the young entrepreneur chooses portfolio allocations given total savings, st E. The fraction φt E of savings is invested in capital, such that Kt+1 E = φ t E st E N t, where Kt+1 E = k t+1 E N t+1 is total E-firm capital. The remaining (1 φt E ) fraction of savings is invested in housing, such that Pt H Ht E = ( ) 1 φt E s E t N t, where Ht E denotes the total housing stock purchased by young entrepreneurs in period t. Throughout this paper, we ensure that there exists an interior solution for the portfolio choice, such that the following no-arbitrage condition holds: (8) P H t+1 P H t = ρ E t+1, where ρ E t+1 = ρ E (a constant) during the transition. Hence, an old entrepreneur s income is simply ρ E s E t. The above condition simply says that the entrepreneur s rate of return to

16 VOL. VOL NO. ISSUE THE GREAT HOUSING BOOM OF CHINA 15 housing and rate of return to capital must be equal in a bubbly equilibrium. THE BANK S PROBLEM. For expositional purpose, we assume that for each period the bank simply absorbs deposits from young workers, lends out to F-firms at interest rate R, and invests the rest in foreign bonds with the same rate of return R (as in SSZ, 2011). The resulting housing price dynamics would be similar if we instead allowed the bank to invest in housing on behalf of the workers with two additional assumptions: (i) the bank s only source of funding is the household deposit (although they can lend to foreigners by investing in foreign bonds); 24 and (ii) the bank is required to provide funds to meet the capital demand of F-firms before they can invest in housing. 25 Accordingly, the demand for housing by state banks or F-firms is simply a fraction of household savings after meeting F-firm capital demand. Since banks are borrowing constrained in the international capital market, this ensures that banks or F-firms are not the marginal investors. TIMELINE. To summarize, in each period economic events unfold as follows: 1) At the beginning of period t, E-firms and F-firms produce. Each young worker gets paid a real wage, w t, regardless of which sector the young worker works in. Each young entrepreneur gets m t. 2) Both the young entrepreneur and young worker make consumption and savings decisions. In addition, the young entrepreneur makes a portfolio choice, φ E t. 3) The housing market opens. The old entrepreneur sells housing stock held in the previous period, H E t 1. The young entrepreneur makes a portfolio decision, φ E t. 4) F-firms repay their capital rents to the bank. 5) The currently old workers and entrepreneurs consume and die. LAW OF MOTION. Since the E-firm is self-financed, the law of motion for E-firm capital stock follows (9) K E t+1 = φ E t ρ E t ψ (1 ψ) α β 1 K E t, 24 The Chinese government has strict control over capital inflow other than foreign direct investment (e.g., foreign borrowing or allowing foreigners to purchase houses). Specifically, portfolio investment is controlled by quotas and foreign borrowing is subject to a ceiling (for short-term borrowing) or approval requirements (for long-term borrowing). Accordingly, during , the overall non-foreign-direct-investment capital account has on average a net outflow of 0.2 percent of GDP (Bayoumi and Ohnsorge, 2013). 25 In China, an important task for state-owned banks is to finance SOE production to maintain employment and thus social stability (see Bai, et al., 2000).

17 16 AMERICAN ECONOMIC JOURNAL MONTH YEAR where ρt E = ρ E for all periods during the transition. As shown later, in this simple economy, the entrepreneur s portfolio share in physical capital, φt E, is constant, which together with a constant ρ E implies that the dynamics of the model have an AK feature during the transition: the growth rate of E-firm capital is constant. Similarly, we can obtain the implicit law of motion for housing demand as: (10) Pt H H = ( ) 1 φt E ρt E ψ 1 (1 ψ) α 1 + β 1 K t E, where we have used the housing market-clearing condition, H E t = H. POST-TRANSITION EQUILIBRIUM. We now characterize the equilibrium in the posttransition stage. Since nt E = 1, E-firm profit is (11) π ( k E t ) = α (1 ψ) ( k E t ) α (At χ) 1 α. Note that π ( ) kt E features decreasing returns to scale at this stage. The rate of return to E-firm capital is simply ρt+1 E = α (1 ψ) ( kt+1) E α 1 (At+1 χ) 1 α. THE STEADY STATE. The steady state of the economy is reached only in the posttransition stage. Since all per capita variables (except labor inputs and housing) grow at the rate A t, we detrend them as x t = x t /A t. At the steady state, the law of motion for capital (9) implies (12) k E = [ ] ψφ E 1 χ 1 α 1 α ( ). 1 + β 1 (1 + z) (1 + ν) Since ρ E = α (1 ψ) ( k E /χ ) α 1, we have (13) ρ E = α (1 ψ) ( 1 + β 1 ) (1 + z) (1 + ν) ψφ E. Equation (13) implies that the rate of return to capital is negatively related to the E-firm portfolio share in physical capital, φ E. The equilibrium portfolio allocation φ E can be solved by the no-arbitrage condition. Since the supply of housing is fixed, the growth rate of housing prices, denoted as ρt+1 H P t+1 H /P t H, equals the balanced growth rate, (1 + z) (1 + ν), in the steady state. As a result, the no-arbitrage condition implies the E-firm steady-state portfolio share in physical capital is: (14) φ E = α (1 ψ) ( 1 + β 1) /ψ.